Some Inequalities in Functional Analysis, Combinatorics, and Probability Theory

Chunrong Feng, Liangpan Li, Jian Shen

Abstract

The main purpose of this paper is to show that many inequalities in functional analysis, probability theory and combinatorics are immediate corollaries of the best approximation theorem in inner product spaces. Besides, as applications of the de Caen-Selberg inequality, the finite field Kakeya and Nikodym problems are also studied.